Electric UAV propulsion systems have an advantage over fuel-powered UAVs. As the "heart" of an electric UAV, the remaining service life prediction of its electrical system is an important estimation parameter in battery health management. In this paper, we propose a data-driven incremental prediction method that integrates empirical modal decomposition and incremental learning models. First, a stochastic configuration network (SCN)-based incremental prediction model is designed to update the model input parameters by adding new data to overcome the in-flight data variation and employing Decay Regularization (DR) to avoid the output weight overfitting problem. Then, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is introduced to perform nonlinear mode decomposition on the UAV battery service data. Finally, experiments are conducted on the NASA UAV battery dataset. The experimental results show that the proposed CEEMDAN-DRSCN has good prediction performance and stability, prediction error is as low as 0.0004.